Factorial Analysis of the Specialization in Habitat Selection Studies. Unpublished Work of James Dunn (University of Arkansas)

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Description

dunnfa performs a factorial decomposition of the Mahalanobis distances in habitat selection studies (see details).

Usage

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dunnfa(dudi, pr, scannf = TRUE, nf = 2)
## S3 method for class 'dunnfa'
print(x, ...)

Arguments

dudi

an object of class pca

pr

a vector giving the utilization weights associated to each unit

scannf

logical. Whether the eigenvalues barplot should be displayed

nf

an integer indicating the number of kept axes

x

an object of class dunnfa

...

additional arguments to be passed to the function print

Details

This analysis is in essence very similar to the MADIFA (see ?madifa). The Mahalanobis distances are often used in the context of niche-environment studies (Clark et al. 1993, see the function mahasuhab). Each resource unit takes a value on a set of environmental variables. Each environmental variable defines a dimension in a multidimensionnal space, namely the ecological space. A set of points (resource units) describes what is available to the species. For each point, a "utilization weight" measures the intensity of use of the point by the species. The set of points for which the utilization weight is greater than zero defines the "niche". The Mahalanobis distance between any resource unit in this space (e.g. the point defined by the values of environmental variables in a pixel of a raster map) and the centroid of the niche (the distribution of used resource units) can be used to give a value of eccentricity to this point.

For a given distribution of available resource units, for which a measure of Mahalanobis distances is desired, the MADIFA (MAhalanobis DIstances Factor Analysis) partitions the ecological space into a set of axes, so that the first axes maximises the average proportion of their squared Mahalanobis distances. James Dunn (formerly University of Arkansas) proposed the analysis programmed in the function dunnfa, as an alternative to the MADIFA (unpublished results). This analysis is closely related to both the ENFA (Ecological niche factor analysis, Hirzel et al. 2002) and the MADIFA.

The analysis proposed by James Dunn searches, in the multidimensional space defined by environmental variables, synthesis variables which maximise the ratio (variance of the scores of available resource units) / (variance of the scores of used resource units). This ratio is sometimes called "specialization" in the ecological literature (Hirzel et al. 2002). It is therefore very similar to the ENFA (which also maximises the specialization), except that the factorial axes returned by this analysis are not required to be *orthogonal to the marginality axis*.

James Dunn demonstrated that this analysis also partitions the Mahalanobis distances into uncorrelated axes, which makes it similar to the MADIFA (the difference is that the MADIFA maximises the mean squared Mahalanobis distances on the first axes, whereas the DUNNFA maximises the specialization on the first axes). Therefore, as for the MADIFA, the DUNNFA can be used to build reduced rank habitat suitability map.

Note that although this analysis could theoretically be used with all kinds of variables, it it currently implemented only for numeric variables.

Value

dunnfa returns a list of class dunnfa containing the following components:

call

original call.

tab

a data frame with n rows and p columns (original data frame centered by column for the uniform weighting).

pr

a vector of length n containing the number of points in each pixel of the map.

nf

the number of kept axes.

eig

a vector with all the eigenvalues of the analysis.

liA

row coordinates (centering on the centroid of the cloud of available points), data frame with n rows and nf columns.

liU

row coordinates (centering on the centroid of the cloud of available points), data frame with p rows and nf columns.

mahasu

a vector of length n containing the reduced-rank squared Mahalanobis distances for the n units.

co

column (environmental variables) coordinates, a data frame with p rows and nf columns

cor

the correlation between the DUNNFA axes and the original variable

Note

This analysis was developed by James Dunn during an e-mail discussion on the MADIFA, and is still unpublished work. Implemented in adehabitatHS with his autorization.

Author(s)

Clement Calenge clement.calenge@oncfs.gouv.fr

References

Clark, J.D., Dunn, J.E. and Smith, K.G. (1993) A multivariate model of female black bear habitat use for a geographic information system. Journal of Wildlife Management, 57, 519–526.

Hirzel, A.H., Hausser, J., Chessel, D. & Perrin, N. (2002) Ecological-niche factor analysis: How to compute habitat-suitability maps without absence data? Ecology, 83, 2027–2036.

Calenge, C., Darmon, G., Basille, M., Loison, A. and Jullien J.M. (2008) The factorial decomposition of the Mahalanobis distances in habitat selection studies. Ecology, 89, 555–566.

See Also

madifa, enfa and gnesfa for related methods. mahasuhab for details about the Mahalanobis distances.

Examples

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## Not run: 
data(bauges)

map <- bauges$map
locs <- bauges$loc

## We prepare the data for the analysis
tab <- slot(map, "data")
pr <- slot(count.points(locs, map), "data")[,1]

## We then perform the PCA before the analysis
pc <- dudi.pca(tab, scannf = FALSE)
(dun <- dunnfa(pc, pr, nf=2,
               scannf = FALSE))

## We should keep one axis:
barplot(dun$eig)

## The correlation of the variables with the first two axes:
s.arrow(dun$cor)

## A factorial map of the niche (centering on the available points)
scatterniche(dun$liA, dun$pr, pts=TRUE)

## a map of the reduced rank Mahalanobis distances
## (here, with one axis)
dun2 <- dunnfa(pc, pr, nf=1,
              scannf = FALSE)
df <- data.frame(MD=dun2$mahasu)
coordinates(df) <- coordinates(map)
gridded(df) <- TRUE
image(df)


## Compute the specialization on the row scores of
## the analysis:
apply(dun$liA, 2, function(x) {
   varav <- sum((x - mean(x))^2) / length(x)
   meanus <- sum(dun$pr*x)/sum(dun$pr)
   varus <- sum(dun$pr * (x - meanus )^2)/sum(dun$pr)
   return(varav/varus)
})
## The eigenvalues:
dun$eig


## End(Not run)

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